Geologic models are commonly used in the petroleum exploration and production industry to characterize petroleum reservoirs and depositional basins. The term “geologic model” may represent either the entire volume of a subsurface volume of interest to an analyst, or a single region of interest within that larger subsurface volume. Geologic models are generally in the form of a three-dimensional array of blocks, sometimes referred to as cells. Furthermore, geologic modeling techniques frequently refer to nodes within a model; each such node generally falls at the center of any such block or cell. Occasionally models are in the form of an array of points, in which case each point is a node. However, hereafter, without limitation, geologic models will be referred to as being constructed of an array of blocks.
A geologic model's characterization of the subsurface derives from the assigning of geologic rock properties, such as lithology, porosity, acoustic impedance, permeability, and water saturation, to each of the blocks in the model. The process of assigning values to the blocks is generally constrained by stratigraphic or structural surfaces and boundaries, such as facies changes, that separate regions of different geologic and geophysical properties within the subsurface. Because geologic models are frequently used to simulate the performance of a reservoir over time, the importance of accurately assigning the values to each of the blocks results from the fact that the spatial continuity of the rock properties in a petroleum reservoir can significantly influence fluid flow from the reservoir. More accurate geologic model characterizations of rock-property spatial continuity allow more accurate planning of the production that can be attained from the reservoir. For this reason, methods of improving the accuracy of the characterization of rock-property spatial continuity in geologic models are desired.
Industry presently uses geostatistical algorithms to characterize the three-dimensional spatial continuity of a rock property in a geologic model. These algorithms use a variogram to quantify the spatial variability of the rock property as a function of both separation distance and direction between individual blocks in the model. Another form of geostatistical simulation is spectral simulation, which uses the amplitude spectrum to control the three-dimensional continuity of rock properties within the model. The amplitude spectrum is the frequency-domain representation of the variogram. There are several advantages of spectral simulation over more traditional geostatistical simulation methods that use variograms. These advantages include computation speed, particularly when using the fast Fourier transform, and the ability to directly measure and model rock-property continuity as a function of continuity scale (spectral frequency), a feature unique to spectral simulation.
Nevertheless, all geostatistical algorithms, including spectral simulation, at present suffer from the limiting assumption of stationarity in the geologic characteristics of the modeled subsurface region. In other words, geostatistical algorithms assume that a modeled rock property can be represented by a single set of statistical measures, which are often referred to as global measures. For example, a single global variogram model or amplitude spectrum would be used to represent the spatial continuity of the modeled rock property over all blocks of the entire model. The variogram or spectrum defines both the desired range (magnitude or separation distance) and dominant direction of the continuity, assuming an anisotropic model. A limitation of this method, however, is that it is well known in the art that the geologic characteristics of the subsurface are non-stationary. Specifically, the spatial continuity of a rock property may change locally within the model, sometimes according to predictable or measurable trends. These local changes will be referred to as local measures, and may be characterized by local variogram models.
For example, consider the sediments deposited in a river channel. Paleo-hydrodynamics control the distribution of the lithological and petrophysical properties within this channel. It is understood in the art that the continuity of these properties is anisotropic—typically greatest along the channel and less continuous across channel. It is also understood that sinuosity may cause channel reaches to locally vary in direction; therefore, rock-property continuity will also locally vary in direction. Most geostatistical methods do not allow the direction of continuity to vary spatially, but instead impose the limitation of a single direction of maximum continuity on the model.
Very few geostatistical modeling methods have attempted to address this limitation. Xu (1996) developed a geostatistical algorithm that can model locally varying orientations of the rock properties. When assigning a rock-property value to a geologic-model block, the variogram orientation is rotated to match the local orientation of rock-property continuity. Azimuths assigned to each geologic model block represent this local orientation. Azimuths are distances in angular degrees, generally in a clockwise direction from north. These azimuths may be obtained from any source, including well or seismic data interpretation. However, when assigning a property value to a geologic-model block, this method must assume an identical local orientation of rock-property continuity for all blocks within the local search radius, even if the azimuths differ for each block. This limits the ability to model locally rapid changes in continuity orientation. In addition, the method is a variant of traditional geostatistical algorithms that use variograms and, as compared to spectral simulation, suffers from the limitations noted above.
More recently, Jones et al. described, in a co-pending patent application titled “Method for Locally Varying Spatial Continuity in Geologic Models,” a method of building geologic models in which the direction of greatest continuity bends spatially according to geologic or geophysical interpretation. This interpretation leads to the path and orientation of maximum continuity, defined by a thalweg. A thalweg is a reference line, often a centerline, through an interpreted geologic feature, such as a seismically interpreted channel complex. The fundamental idea behind the method is to transform the coordinate system prior to modeling so that the thalweg is linear in a new coordinate system. Standard geostatistical methods may be used in the new coordinate system, which then involves a constant orientation of continuity. After geostatistical simulation, the original coordinate system is restored, providing a model in which continuity follows the path of the thalweg. This invention works well to condition rock-property continuity in geologic features that can be associated with and described by a single thalweg; i.e., features with continuity directions that align with a single thalweg, such as a channel feature. However, the invention does not work well to condition rock-property continuity in geologic features or regions having more complex continuity patterns; i.e., features with continuity directions that cannot be defined by a single thalweg, such as a complex deltaic geometry.
There is a need for a method whereby the direction of maximum continuity within a random field, such as a three-dimensional geologic model, can be locally varied. More specifically, there is a need for a method which allows the modeler to vary the direction of maximum rock-property continuity at any location in the geologic model according to local azimuth and/or dip information, using spectral simulation as the geostatistical modeling method. Any such method should allow use of information from geologic or geophysical data to determine or deduce the extent to which continuity locally varies in a specific direction within the modeled region of the subsurface, and thereby provide the ability to accurately represent this variability within the geologic model and to simulate reservoir flow performance which reflects this variability. The present invention satisfies that need.